Презентация, доклад University physics. Forces review of basic concepts


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University Physics I Forces Review of Basic Concepts

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Vectors and Scalars All physical quantities (e.g. speed and force) are described by a magnitude and a unit. VECTORS – also need to have their direction specified examples: displacement, velocity, acceleration, force. SCALARS – do not have a direction examples: distance, speed, mass, work, energy.


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Representing Vectors An arrowed straight line is used. The arrow indicates the direction and the length of the line is proportional to the magnitude.

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Addition of vectors 1

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Addition of vectors 2 With two vectors acting at an angle to each other: Draw the first vector. Draw the second vector with its tail end on the arrow of the first vector. The resultant vector is the line drawn from the tail of the first vector to the arrow end of the second vector. This method also works with three or more vectors.

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Resultant of Two Forces

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Addition of Vectors

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Addition of Vectors

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Resultant of Several Concurrent Forces

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Rectangular Coordinate System

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Direction Angles

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Relationships for Direction Angles

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Example 1. A force has x, y, and z components of 3, 4, and –12 N, respectively. Express the force as a vector in rectangular coordinates.

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Determine the magnitude of the force in previous example:

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Determine the three direction angles for the force :

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Vector Operations to be Considered Scalar or Dot Product: A•B Vector or Cross Product: AxB Triple Scalar Product: (AxB)•C

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Consider two vectors A and B oriented in different directions.

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Scalar or Dot Product

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First Interpretation of Dot Product: Projection of A on B times the length of B.

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Or alternatively: Projection of B on A times the length of A.

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Some Implications of Dot Product

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Example : Perform several scalar operations on the following vectors:

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Vector or Cross Product


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